I’ll bet I can gain access after two dozen tries

With a very lucky guess, I have actually pulled this off once in two tries, and got many free beers by people stunned by my “elite hacker skills”.

My assertion that it would take me 24 (4 × 3 × 2 × 1) attempts to enter the correct keycode is based on a few reasonable assumptions:

the keycode is 4 digits long, as many are (people complain if you try to make them longer)

I can try three keycodes at a time without locking myself out of more attempts, wait a couple of minutes, and try another three keycodes, wait a couple of minutes, and so on, and

the wear marks on the keypad are real and not a ruse to throw off would-be thieves.

It might be interesting to use fake wear marks on a keypad as a kind of honeypot. You could have the system send an alert if someone kept entering keycodes that were permutations of numbers corresponding to the keys with fake wear.